Позитивные изменения. Том 3, № 4 (2023). Positive changes. Volume 3, Issue 4(2023)

Source: STATA 17.0 Output, 2023.

Legend: Except for SRQ and CSIZE where p-value>0.05

Additionally, post-estimation tests for data normality (Skewness/Kurtosis and Shapiro-Wilk), the Breusch and Pagan Lagrange Multiplier, contemporaneous correlation, panel serial correlation, and group-wise heteroscedasticity were performed. Table IV presents an overview of the findings from these testing.

Table 5. Regression Results

Source: STATA 17.0 Output, 2023.

Legend: Coefficients: ** P-value <.01; * P-value <.05.

The skewness/kurtosis and Shapiro-Wilk tests are run on the FE regression residuals to determine whether or not the study’s data is normally distributed. Based on the findings in Table IV, each joint adjusted Chi2 has a skewness/kurtosis alpha value that is less than 0.05 (with the exception of SRQ and CSIZE), suggesting that the majority of the variables provide a z-statistic that is larger than 1.96 as a whole. This suggests that the study’s data is biased (not symmetrical). Similarly, the Shapiro-Wilk z-scores fall outside the bracket of +/-1.96, all of which are significant at p-values less than 0.05, which indicates that data for the variables is not normally distributed.

The presence of serial correlation in the panels makes the idiosyncratic errors terms of the coefficients to become smaller than their actual state, while the R² is higher (Wooldridge, 2002). Based on the evidence in Table IV, which shows an F-value of 16.754 and a p-value of 0.0027, which suggests the presence of serial correlation in the panel data’s structure, the null hypothesis of “no serial correlation” cannot be supported.

In addition, the study conducts Pesaran’s cross-sectional test of independence to ascertain the correlation of residuals or otherwise across the sampled companies. This is due to the presence of contemporaneous correlations also known as cross-sectional dependence among residuals of the models amounts to bias the estimates. The study’s null hypothesis is that there is no correlation between residuals at a 5-percent level of significance. For the test with a p-value of 0.1296, Table IV shows the Chi2 to be 1.516. With this supporting the null hypothesis, the study comes to the conclusion that the model residuals are not associated.

Furthermore, the study conducts the group-wise heteroscedasticity using residuals of the generalized least square (GLS) regression and based on the modified Wald statistic. This is because, based on the assumption of homoscedasticity across residuals, the presence of heteroscedasticity leads to bias among standard errors of the estimates. The regression models’ residuals being homoscedastic at a 5-percent level of significance is the null hypothesis for this test. Based on the significant Chi2 of 1875.31, with a p-value of 0.000 as presented in Table IV, the study fails to support the null hypothesis but concludes that residuals of the models are heteroscedastic.

As mentioned above, the Shapiro-Wilk and skewness/kurtosis test findings show that outliers exist within the conventional residuals of the FE regression. Data transformation, however, is not an option because the study’s explanatory variables, which are based on the VIF, do not exhibit multicollinearity. In the same vein, the presence of contemporaneous correlation, panel serial correlation and groupwise heteroskedasticity in the panel adversely affect parameter estimates and bias standard errors (Cameron, 2009). Therefore, to correct these abnormalities and ensure the estimation of parameter coefficients are consistent, efficient and standard error bias-free, the study adopts Panel Corrected Standard Error (PCSE) estimate as suggested in Beck and Katz (1996, 1995).

SRQ_i,t = β₀ + β₁SCSIZE_i,t + β₂SCINDEP_i,t + β₃SCDIV_i,t + β₄SCDIL_i,t + β₅CSIZE_i,t + ε_i,t  (1)

Table 6. Test of Research Hypotheses

Source: STATA 17.0 Output, 2023.

Legend: * P-value <.01; * P-value <.05.

Table 5 contains the z-scores, p-values and PCSEs of each predictor variable on the dependent variables. It is based on the model restated thus:

The PCSE result for the GLS model shows an R2 of 10.84 percent compared to the total R2 of 30.12 percent for the FE model, showing a significant fall of 19.28 percent. With a significant p-value of 0.000 and a Wald Chi2 of 43.11, Table V shows that the model is fit for the data and that the combined contribution of businesses from the two nations strongly explains differences in SRQ.